, Volume 16, Issue 1, pp 42–45 | Cite as

The determination of mode shapes for dynamically loaded rigid-plastic structures

  • J. B. Martin


Mode solutions in rigid-plastic structures subjected to fixed external loads are dynamic solutions which are products of separate functions of space and time. If the small displacement assumptions are adopted, there will exist at least one mode shape for any structure subjected to given fixed external load, and possibly a multiplicity of modes. The time function is a simple linear function, and is easily determined once the mode shape is known. The paper puts forward, a simple in physical terms, algorithm for the determination of mode shapes. An iterative procedure is established in which each iteration is equivalent to the solution of a static limit analysis problem. Convergence is proved.


Linear Function Civil Engineer Alla Tempo Static Limit 
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Soluzioni modali per strutture rigido-plastiche soggette a carichi esterni fissi sono soluzioni dinamiche rappresentabili come prodotti di funzioni separate delle variabili spaziali e del tempo. Nell'ipotesi di piccoli spostamenti, esiste almeno una configurazione modale o «modo» per una struttura soggetta a dati carichi esterni fissi e può esserci una moltiplicità di modi. La funzione del tempo è una funzione lineare che può essere facilmente determinata qualora sia noto il modo. Questo lavoro propone un metodo, semplice dal punto di vista meccanico, per il calcolo di configurazioni modali. Si sviluppa un procedimento iterativo in cui ciascuna iterazione equivale alla soluzione di un problema statico di analisi limite, e se ne dimostra la convergenza.


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Copyright information

© Pitagora Editrica Bologna 1981

Authors and Affiliations

  • J. B. Martin
    • 1
  1. 1.Departement of Civil EngineeringUniversity of Cape TownSouth Africa

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